Measurement optimization of variational quantum simulation by classical shadow and derandomization
Measurement optimization of variational quantum simulation by classical shadow and derandomization
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DOI：
10.22331/q-2023-05-04-995
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发表时间：
2022-08
期刊：
影响因子：
6.4
通讯作者：
Kouhei Nakaji;Suguru Endo;Y. Matsuzaki;H. Hakoshima
中科院分区：
文献类型：
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作者：
Kouhei Nakaji;Suguru Endo;Y. Matsuzaki;H. Hakoshima
模拟大型量子系统是量子计算的最终目标。变分量子模拟（VQS）为我们提供了一种工具，通过将计算负载分配给经典计算机和量子计算机来实现近期设备的目标。然而，随着量子系统规模变大，VQS 的执行变得越来越具有挑战性。最严峻的挑战之一是测量数量的急剧增加；例如，在化学哈密顿量的量子模拟中，测量数量往往会增加量子位数量的四次方。这项工作的目的是通过最近提出的基于阴影的策略（例如经典阴影和去随机化）来显着减少 VQS 中的测量数量。尽管之前的文献表明基于影子的策略成功地优化了变分量子优化（VQO）中的测量，但由于 VQO 和 VQS 在测量可观测值方面存在差距，如何将其应用于 VQS 尚不清楚。在本文中，我们通过改变 VQS 中测量可观测值的方式来弥补这一差距，并提出一种通过基于影子的策略来优化 VQS 中测量的算法。我们的理论分析不仅揭示了在 VQS 中使用我们的算法的优势，而且理论上支持在 VQO 中使用基于影子的策略，其优势仅在数值上给出。此外，我们的数值实验表明了在量子化学系统中使用我们的算法的有效性。
Simulating large quantum systems is the ultimate goal of quantum computing. Variational quantum simulation (VQS) gives us a tool to achieve the goal in near-term devices by distributing the computation load to both classical and quantum computers. However, as the size of the quantum system becomes large, the execution of VQS becomes more and more challenging. One of the most severe challenges is the drastic increase in the number of measurements; for example, the number of measurements tends to increase by the fourth power of the number of qubits in a quantum simulation with a chemical Hamiltonian. This work aims to dramatically decrease the number of measurements in VQS by recently proposed shadow-based strategies such as classical shadow and derandomization. Even though previous literature shows that shadow-based strategies successfully optimize measurements in the variational quantum optimization (VQO), how to apply them to VQS was unclear due to the gap between VQO and VQS in measuring observables. In this paper, we bridge the gap by changing the way of measuring observables in VQS and propose an algorithm to optimize measurements in VQS by shadow-based strategies. Our theoretical analysis not only reveals the advantage of using our algorithm in VQS but theoretically supports using shadow-based strategies in VQO, whose advantage has only been given numerically. Additionally, our numerical experiment shows the validity of using our algorithm with a quantum chemical system.